Initial implementation of interpolation matrix generation for TensorMesh (3D ONLY)

SimPEG/utils/__init__.py

@@ -1,7 +1,9 @@
 import matutils
 import sputils
 import lomutils
+import interputils
 import ModelBuilder
 from matutils import getSubArray, mkvc, ndgrid, ind2sub, sub2ind
 from sputils import spzeros, kron3, speye, sdiag
 from lomutils import volTetra, faceInfo, inv2X2BlockDiagonal, inv3X3BlockDiagonal, indexCube, exampleLomGird
+from interputils import interpmat

SimPEG/utils/interputils.py

@@ -0,0 +1,77 @@
+import numpy as np
+import scipy.sparse as sp
+from sputils import spzeros
+from matutils import mkvc, sub2ind
+
+def interpmat(x,y,z,xr,yr,zr):
+
+    """ Local interpolation computed for each receiver point in turn """
+
+    nx = max(x.shape)
+    ny = max(y.shape)
+    nz = max(z.shape)
+    npts = max(xr.shape)
+
+    Q = sp.lil_matrix((npts, nx*ny*nz))
+
+    for i in range(npts):
+        # in x-direction   
+        im = np.argmin(abs(x-xr[i]))
+        if  xr[i] - x[im] >= 0:  # Point on the left
+            ind_x1 = im
+            ind_x2 = im+1
+        elif  xr[i] - x[im] < 0:  # Point on the right
+            ind_x1 = im-1
+            ind_x2 = im        
+        dx1 = xr[i] - x[ind_x1]
+        dx2 = x[ind_x2] - xr[i]
+        # in y-direction
+        im = np.argmin(abs(y-yr[i]))
+        if  yr[i] - y[im] >= 0:  # Point on the left
+            ind_y1 = im
+            ind_y2 = im+1
+        elif  yr[i] - y[im] < 0:  # Point on the right
+            ind_y1 = im-1
+            ind_y2 = im        
+        dy1 = yr[i] - y[ind_y1]
+        dy2 = y[ind_y2] - yr[i]    
+        # in z-direction
+        im = np.argmin(abs(z-zr[i]))
+        if  zr[i] - z[im] >= 0:  # Point on the left
+            ind_z1 = im
+            ind_z2 = im+1
+        elif  zr[i] - z[im] < 0:  # Point on the right
+            ind_z1 = im-1
+            ind_z2 = im        
+        dz1 = zr[i] - z[ind_z1]
+        dz2 = z[ind_z2] - zr[i]    
+        dv = (x[ind_x2] - x[ind_x1]) * (y[ind_y2] - y[ind_y1]) *(z[ind_z2] - z[ind_z1])
+
+        Dx =  x[ind_x2] - x[ind_x1]
+        Dy =  y[ind_y2] - y[ind_y1]
+        Dz =  z[ind_z2] - z[ind_z1]
+
+        # Get the row in the matrix
+
+        inds = sub2ind((nx,ny,nz),[ 
+            ( ind_x1,  ind_y2,  ind_z1),
+            ( ind_x1,  ind_y1,  ind_z1),
+            ( ind_x2,  ind_y1,  ind_z1),
+            ( ind_x2,  ind_y2,  ind_z1),
+            ( ind_x1,  ind_y1,  ind_z2),
+            ( ind_x1,  ind_y2,  ind_z2),
+            ( ind_x2,  ind_y1,  ind_z2),
+            ( ind_x2,  ind_y2,  ind_z2)])
+        
+        vals = [(1-dx1/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
+                (1-dx1/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
+                (1-dx2/Dx)*(1-dy1/Dy)*(1-dz1/Dz),
+                (1-dx2/Dx)*(1-dy2/Dy)*(1-dz1/Dz),
+                (1-dx1/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
+                (1-dx1/Dx)*(1-dy2/Dy)*(1-dz2/Dz),
+                (1-dx2/Dx)*(1-dy1/Dy)*(1-dz2/Dz),
+                (1-dx2/Dx)*(1-dy2/Dy)*(1-dz2/Dz)]
+
+        Q[i, mkvc(inds)] = vals
+    Q = Q.tocsr()
+    return Q